Open the video in MPlayerX and pause it. Drag the timeline slider to the desired starting point (keep it all the way left to start from the begginiing at time 0:00). Click Playback in the menubar > A-B Loop > Set Start Point.

Then, drag the timeline slider to the ending point (or all the way right if you want to loop the entire video). Go to Playback > A-B Loop > Set Return Point.

I can't find a menu, preference option, or any mention on the support page or change logs for a looping option, so I think it might be safe to say no, there isn't a way to do that with that piece of software.